Understand the idea.
What does the box stand for?
A box or question mark stands for an unknown number. First decide whether it represents a part or the whole. In , the whole is known and the missing number is the other added part.
To find a missing whole, add the known parts. To find a missing part, subtract the known part from the whole. A quick part–whole sketch can help you choose before calculating.
A missing starting number
In , the starting whole is missing. The is what remains after removing , so add those two parts to rebuild the starting number: .
In , the whole is already given; the removed part is missing. Subtract from to find it. Put your answer back into the original sentence and check both sides agree.
See the method in action.
Find a missing added part
Find the missing number: 157 + ? = 300.
Worked solution
- 1
Find the missing part by subtraction.
The whole is three hundred and one of its parts is one hundred and fifty-seven.
- 2
Remove one hundred, then fifty.
These are the first two parts of one hundred and fifty-seven.
- 3
Remove the final seven.
All of the known part has now been subtracted.
- 4
Substitute the missing number.
The two added parts give the required whole.
143
Find a missing start
Find the missing number: ? − 67 = 125.
Worked solution
- 1
Rebuild the missing starting whole.
Add the removed sixty-seven to the remaining one hundred and twenty-five.
- 2
Add sixty, then seven.
Sixty and seven together make sixty-seven.
- 3
Check in the original subtraction.
Removing the given amount leaves the required remainder.
192
Try it yourself.
Check your understanding
Find ?: ? − 19 = 42.
Show answer & reasoning
61
The missing starting number must contain both the remaining and removed . Add ; checking gives .
Keep practising
6 worksheet questions
Read the questions online
- Find ?: .
- Find ?: .
- Find ?: .
- Find ?: .
- A bus starts with some people. Twelve get off and 27 remain. How many were on the bus at the start?
- Find a number that makes this equation true: .
Read the worked solutions
- Find ?: .
; check .
32 - Find ?: .
.
79 - Find ?: .
; check .
36 - Find ?: .
; check .
212 - A bus starts with some people. Twelve get off and 27 remain. How many were on the bus at the start?
; .
39 people - Find a number that makes this equation true: .
First find the right side: . Then . Check both sides equal 50.
25
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Mental strategies; two-/three-digit calculations; regrouping; inverse operations; missing values.
Official curriculum source ↗